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Multivariate Stochastic Volatility with Cross Leverage

  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

We describe and estimate for the first time a natural multivariate extension of the univariate stochastic volatility model with leverage. The model, which we call the multivariate stochastic volatility with cross leverage, is fit by a tuned Bayesian MCMC method. Of particular general interest is our approach for sampling the state variables from the posterior distribution conditioned on the parameters. The state variables are sampled in blocks by the Metropolis-Hastings algorithm in which the proposal density is derived from an approximating linear Gaussian state space model. The conditional modes of the latent volatility variables are computed using a method of scoring where the covariance matrix of the proposal density is guaranteed to be positive definite. The auxiliary particle filter to compute the likelihood function is also shown and the model and the techniques are illustrated with daily stock returns data from the Tokyo Stock Exchange.

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Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-191.

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Length: 19 pages
Date of creation: Nov 2009
Date of revision:
Handle: RePEc:cfi:fseres:cf191
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